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Chapter 10: Problem 63

Explain how to find or probabilities with events that are not mutually exclusive. Give an example.

Short Answer

Expert verified
The probability of non-mutually exclusive events A or B occurring can be found by using the formula P(A or B) = P(A) + P(B) - P(A and B). As an example, the probability of drawing a King or a Red card from a standard deck of cards is 7/13.

Step by step solution

01

Introduction to probabilities

Probability is a statistical measure that shows the likelihood of an event to occur. The probability of the occurrence of an event A can be found by dividing the number of ways event A can occur, by the total number of outcomes.
02

Understanding non-mutually exclusive events

Two events are non-mutually exclusive if they can occur at the same time. For example, if you draw a random card from a deck, getting a king and getting a red card are non-mutually exclusive events since the drawn card can be a red king.
03

Formula for non-mutually exclusive events

The formula to calculate the probability of occurence of non-mutually exclusive events A or B is given by P(A or B) = P(A) + P(B) - P(A and B). In this formula, P(A) and P(B) are the probabilities of occurrence of events A and B separately, while P(A and B) is the probability of both events occurring together.
04

Example to find or probabilities with events that are not mutually exclusive

Consider a standard deck of cards (52 cards: 26 red 鈥� hearts and diamonds 鈥� and 26 black 鈥� clubs and spades). Let's find the probability of drawing a King or a red card. P(King) = 4/52 = 1/13 (since there are 4 Kings), P(Red) = 26/52 = 1/2 (since there are 26 red cards), and P(King and Red) = 2/52 = 1/26 (since there are 2 red Kings). Plugging these into our formula gives us: P(King or Red) = P(King) + P(Red) - P(King and Red) = 1/13 + 1/2 - 1/26 = 7/13.

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